Final answer:
An optimized insertion sort algorithm uses n - 1 comparisons to sort an already sorted list of integers from 1 to n.
Step-by-step explanation:
The student is inquiring about the number of comparisons used by an insertion sort algorithm to sort a list in ascending order, where the list is already sorted and consists of integers from 1 to n. In the best-case scenario, each element from the second one onwards will only need to be compared once to confirm that it is in the correct position. This means for each of the n elements, except the first one, it performs a single comparison, resulting in n - 1 comparisons in total for such an optimized insertion sort algorithm.
Considering that insertion sort compares each new element against already-sorted ones, if the list is already sorted—which is the case with 1, 2, ..., n—it will simply go through the motions of comparing without needing to perform any swaps. Hence, the total number of comparisons would be directly related to the number of elements, which is n, yielding n - 1 comparisons for a completely sorted input list.